falloff_reaction.h

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//-----------------------------------------------------------------------bl-
//--------------------------------------------------------------------------
//
// Antioch - A Gas Dynamics Thermochemistry Library
//
// Copyright (C) 2014-2016 Paul T. Bauman, Benjamin S. Kirk,
//                         Sylvain Plessis, Roy H. Stonger
//
// Copyright (C) 2013 The PECOS Development Team
//
// This library is free software; you can redistribute it and/or
// modify it under the terms of the Version 2.1 GNU Lesser General
// Public License as published by the Free Software Foundation.
//
// This library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
// Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc. 51 Franklin Street, Fifth Floor,
// Boston, MA  02110-1301  USA
//
//-----------------------------------------------------------------------el-

#ifndef ANTIOCH_FALLOFF_REACTION_H
#define ANTIOCH_FALLOFF_REACTION_H

// Antioch
#include "antioch/antioch_asserts.h"
#include "antioch/cmath_shims.h"
#include "antioch/reaction.h"
#include "antioch/kinetics_conditions.h"
#include "antioch/lindemann_falloff.h"
#include "antioch/troe_falloff.h"

//C++
#include <string>
#include <vector>
#include <iostream>

namespace Antioch
{
  template<typename CoeffType=double, typename FalloffType = LindemannFalloff<CoeffType> >
  class FalloffReaction: public Reaction<CoeffType>
  {
  public:

    FalloffReaction( const unsigned int n_species,
                     const std::string &equation, 
                     const bool &reversible = true,
                     const ReactionType::ReactionType &falloffType = ReactionType::LINDEMANN_FALLOFF,
                     const KineticsModel::KineticsModel kin = KineticsModel::KOOIJ);
    
    virtual ~FalloffReaction();

    template <typename StateType, typename VectorStateType>
    StateType compute_forward_rate_coefficient( const VectorStateType& molar_densities,
                                                const KineticsConditions<StateType,VectorStateType>& conditions ) const;
    
    template <typename StateType, typename VectorStateType>
    void compute_forward_rate_coefficient_and_derivatives( const VectorStateType& molar_densities,
                                                           const KineticsConditions<StateType,VectorStateType>& conditions,  
                                                           StateType& kfwd,  
                                                           StateType& dkfwd_dT, 
                                                           VectorStateType& dkfkwd_dX) const;


    const FalloffType &F() const;
    FalloffType &F();

  protected:

    FalloffType _F;

  };

  /* ------------------------- Inline Functions -------------------------*/
  template<typename CoeffType, typename FalloffType>
  inline
  FalloffReaction<CoeffType,FalloffType>::FalloffReaction( const unsigned int n_species,
                                                           const std::string &equation,
                                                           const bool &reversible,
                                                           const ReactionType::ReactionType &falloffType, 
                                                           const KineticsModel::KineticsModel kin)
    :Reaction<CoeffType>(n_species,equation,reversible,falloffType,kin),
     _F(n_species)
     
  {}


  template<typename CoeffType, typename FalloffType>
  inline
  FalloffReaction<CoeffType,FalloffType>::~FalloffReaction()
  {
    return;
  }

  template<typename CoeffType, typename FalloffType>
  inline
  FalloffType &FalloffReaction<CoeffType,FalloffType>::F()
  {
    return _F;
  }

  template<typename CoeffType, typename FalloffType>
  inline
  const FalloffType &FalloffReaction<CoeffType,FalloffType>::F() const
  {
    return _F;
  }

  template<typename CoeffType, typename FalloffType>
  template<typename StateType, typename VectorStateType>
  inline
  StateType FalloffReaction<CoeffType,FalloffType>::compute_forward_rate_coefficient( const VectorStateType& molar_densities,
                                                                                      const KineticsConditions<StateType,VectorStateType>& conditions  ) const
  {
//falloff is k(T,[M]) = k0*[M]/(1 + [M]*k0/kinf) * F = k0 * ([M]^-1 + k0 * kinf^-1)^-1 * F    
    StateType M = Antioch::zero_clone(conditions.T());
    for(unsigned int i = 0; i < molar_densities.size(); i++)
    {
        M += molar_densities[i];
    }

    const StateType k0   = (*this->_forward_rate[0])(conditions);
    const StateType kinf = (*this->_forward_rate[1])(conditions);

    return k0 / (ant_pow(M,-1) + k0 / kinf) * _F(conditions.T(),M,k0,kinf);
  }

  template<typename CoeffType, typename FalloffType>
  template<typename StateType, typename VectorStateType>
  inline
  void FalloffReaction<CoeffType,FalloffType>::compute_forward_rate_coefficient_and_derivatives( const VectorStateType &molar_densities,
                                                                                                 const KineticsConditions<StateType,VectorStateType>& conditions,
                                                                                                 StateType& kfwd, 
                                                                                                 StateType& dkfwd_dT,
                                                                                                 VectorStateType& dkfwd_dX) const 
  {
    //variables, k0,kinf and derivatives
    StateType k0 = Antioch::zero_clone(conditions.T());
    StateType dk0_dT = Antioch::zero_clone(conditions.T());
    StateType kinf = Antioch::zero_clone(conditions.T());
    StateType dkinf_dT = Antioch::zero_clone(conditions.T());

    this->_forward_rate[0]->compute_rate_and_derivative(conditions,k0,dk0_dT);
    this->_forward_rate[1]->compute_rate_and_derivative(conditions,kinf,dkinf_dT);

    StateType M = Antioch::zero_clone(conditions.T());
    for(unsigned int i = 0; i < molar_densities.size(); i++)
    {
        M += molar_densities[i];
    }

    //F
    StateType f = Antioch::zero_clone(M);
    StateType df_dT = Antioch::zero_clone(M);
    VectorStateType df_dX = Antioch::zero_clone(molar_densities);
    _F.F_and_derivatives(conditions.T(),M,k0,dk0_dT,kinf,dkinf_dT,f,df_dT,df_dX);

// k(T,[M]) = k0*[M]/(1 + [M]*k0/kinf) * F = k0 * ([M]^-1 + k0 * kinf^-1)^-1 * F    
    kfwd = k0 / (ant_pow(M,-1) + k0/kinf); //temp variable here for calculations dk_d{T,X}

    StateType temp = (kinf/M + k0);
//dk_dT = F * dkfwd_dT + kfwd * dF_dT
//      = F * kfwd * (dk0_dT/k0 - dk0_dT/(kinf/[M] + k0) + k0 * dkinf_dT/(kinf * (kinf/[M] + k0) ) )
//      + dF_dT * kfwd
    dkfwd_dT = f * kfwd * (dk0_dT/k0 - dk0_dT/temp + dkinf_dT * k0/(kinf * temp))
             + df_dT * kfwd;

    dkfwd_dX.resize(this->n_species(), kfwd);
//dkfwd_dX = F * dkfwd_dX + kfwd * dF_dX
//         = F * kfwd / ([M] +  [M]^2 k0/kinf) + kfwd * dF_dX
    StateType tmp = f * kfwd / (M + ant_pow(M,2) * k0/kinf);
    for(unsigned int ic = 0; ic < this->n_species(); ic++)
      {
        dkfwd_dX[ic] = tmp + df_dX[ic] * kfwd;
      }

    kfwd *= f; //finalize

    return;
  }
  
} // namespace Antioch

#endif // ANTIOCH_FALLOFF_REACTION_H